WASHINGTON — The U.S. is sending more spies, Marines and drones to Libya, trying to speed the search for those who killed the U.S. ambassador and three other Americans, but the investigation is complicated by a chaotic security picture in the post-revolutionary country and limited American and Libyan intelligence resources.

The CIA has fewer people available to send, stretched thin from tracking conflicts across the Middle East, Africa and Asia. Much of the team dispatched to Libya during the revolution had been sent onward to the Syrian border, U.S. officials say.

And the Libyans have barely re-established full control of their country, much less rebuilt their intelligence service, less than a year after the overthrow of dictator Moammar Gadhafi.

The U.S. has already deployed an FBI investigation team, trying to track al-Qaida sympathizers thought to be responsible for turning a demonstration over an anti-Islamic video into a violent, coordinated militant attack on the U.S. Consulate in Benghazi.

Ambassador Chris Stevens and three other embassy employees were killed after a barrage of small arms, rocket-propelled grenades and mortars tore into the consulate buildings in Benghazi on Tuesday, the 11th anniversary of 9/11, setting the buildings on fire.

President Barack Obama said in a Rose Garden statement the morning after the attack that those responsible would be brought to justice. That may not be swift. Building a clearer picture of what happened will take more time and possibly more people, U.S. officials said Friday, speaking on condition of anonymity because they were not authorized to discuss the ongoing investigation publicly.

In a statement posted Saturday on Islamic militant websites, Al-Qaida’s branch in Yemen praised the killings and called for more attacks to expel American embassies from Muslim nations, suggesting the terrorist organization is trying to co-opt the angry protests over a film produced in the United States denigrating the Prophet Muhammad.

Intelligence officials are reviewing telephone and radio intercepts, computer traffic, satellite images and other clues from the days before the attacks - the kinds of material routinely gathered in a conflict zone where al-Qaida affiliates are known to operate - and Libyan law enforcement has made some arrests. But investigators have found no evidence pointing conclusively to a particular group or to indicate the attack was planned, White House spokesman Jay Carney said, adding, “This is obviously under investigation.”

Early indications suggest the attack was carried out not by the main al-Qaida terror group but “al-Qaida sympathizers,” said a U.S. intelligence official, speaking on condition of anonymity because he was not authorized to discuss the investigation publicly.

One of the leading suspects is the Libyan-based Islamic militant group Ansar al-Shariah, led by former Guantanamo detainee Sufyan bin Qumu. The group denied responsibility in a video Friday but did acknowledge its fighters were in the area during what it called a “popular protest” at the consulate, according to Ben Venzke of the IntelCenter, a private analysis firm that monitors Jihadist media for the U.S. intelligence community.

The U.S. had been watching threat assessments from Libya for months but none offered warnings of the Benghazi attack, according to another intelligence official who spoke on condition of anonymity because he was not authorized to speak publicly about U.S. intelligence matters.

Sen. Susan Collins, R-Maine, questioned whether the consulate had taken sufficient security measures, given an attempt to attack the consulate in Benghazi a few months ago.

Carney said that given the 9/11 anniversary, security had been heightened.

“It was, unfortunately, not enough,” he said.

That paucity of resources also applies to the intelligence officers available to monitor Libya on the ground.

With ongoing counterterrorism operations in Afghanistan, Pakistan and Yemen, as well as the civil war in Syria, the CIA’s clandestine and paramilitary officer corps is simply running out of trained officers to send, U.S. officials say, speaking on condition of anonymity because they were not authorized to discuss the deployment of intelligence personnel publicly. The clandestine service is roughly 5,000 officers strong, and the paramilitary corps sent to war zones is only in the hundreds, the officials said.

Most of the CIA’s clandestine and paramilitary team that had worked with Libyan rebels to bring about the fall of Gadhafi is now arrayed at the Syrian border, working with rebels there to try to hasten the fall of Syrian president Bashar Assad, the officials said.

The CIA normally hires extra people to make up for such shortfalls, often retired special operators with the requisite security clearance, military training and language ability. But the government mandate to slash contractor use has meant cutting contracts, according to two former officials familiar with the agency’s current hiring practices.

To fill in the gaps in spies on the ground, the U.S. intelligence community has kept up surveillance over Libya with unmanned and largely unarmed Predator and Reaper drones, increasing the area they cover and the frequency of their flights since the attack on the consulate, as well as sending more surveillance equipment to the region, one official said.

But intelligence gathered from the air still needs corroboration from sources on the ground, as well as someone to act on the intelligence to go after the targets.

The Libyan government, which U.S. officials say is eager to help, has limited tools at its disposal. The post-revolution government has been slow to rebuild both its intelligence capability and its security services, fearful of empowering the very institutions they had to fight to overthrow Gadhafi. They have made a start, but they lack a sophisticated cadre of trained spies and a large network of informants.

“The Libyans in just about every endeavor are just learning to walk, let alone run,” said Paul Pillar, a former senior CIA official and author of the book “Intelligence and U.S. Foreign Policy.”

“There is confusion and competing elements within the new provisional government which complicates the task of creating new institutions, including the intelligence service,” he said.

“There are still some aspects of the intelligence services that still work,” says Barak Barfi of the New America Foundation think tank, including eavesdropping on cellphone calls and spying on computer traffic using equipment from the Gadhafi era. Barfi spent months with members of Libya’s transitional government as they tried to rebuild the nation’s services and infrastructure.

But the Libyans have not yet even taken full command their own security services almost a year after Gadhafi’s fall, Barfi said. That’s given the tens of thousands of militiamen who helped overthrow Gadhafi the time they needed to organize and seek new targets, especially Western ones, he said.

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